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<meta name="citation_issn" content="0009-2614" />
<meta name="citation_volume" content="278" />
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<meta name="citation_publisher" content="North-Holland" />
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<meta name="citation_journal_title" content="Chemical Physics Letters" />
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<meta name="citation_doi" content="10.1016/S0009-2614(97)04014-1" />
<meta name="dc.identifier" content="10.1016/S0009-2614(97)04014-1" />
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<meta property="og:description" content="The Cr2 potential energy curve is obtained by treating the dynamical correlation energy terms using a CI procedure based on determinants, equivalent t…" />
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<meta name="citation_title" content="Epstein-Nesbet second-order perturbation treatment of dynamical electron correlation and ground state potential energy curve of Cr2" />
<meta property="og:title" content="Epstein-Nesbet second-order perturbation treatment of dynamical electron correlation and ground state potential energy curve of Cr2" />
<meta name="citation_publication_date" content="1997/10/31" />
<meta name="citation_online_date" content="1998/04/14" />
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<title>Epstein-Nesbet second-order perturbation treatment of dynamical electron correlation and ground state potential energy curve of Cr2 - ScienceDirect</title>
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Contents" class="preview-sidebar u-show-from-lg col-lg-6"><div class="PreviewTableOfContents text-s"><h2 class="u-h4 preview-table-of-contents-title">Article preview</h2><ul class="preview-table-of-contents-list"><li id="preview-section-abstract-item" class><a class="anchor anchor-default" href="#preview-section-abstract"><span class="anchor-text">Abstract</span></a></li><li id="preview-section-references-item" class><a class="anchor anchor-default" href="#preview-section-references"><span class="anchor-text">References (35)</span></a></li><li id="preview-section-cited-by-item" class><a class="anchor anchor-default" href="#preview-section-cited-by"><span class="anchor-text">Cited by (21)</span></a></li></ul></div></div><article class="col-lg-12 col-md-16 pad-left pad-right" lang="en"><div class="Publication" id="publication"><div class="publication-brand u-show-from-sm"><a class="anchor anchor-default" href="/journal/chemical-physics-letters" title="Go to Chemical Physics Letters on 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href="/journal/chemical-physics-letters/vol/278/issue/4"><span class="anchor-text"><img class="publication-cover-image" src="https://ars.els-cdn.com/content/image/1-s2.0-S0009261424X00020-cov150h.gif" alt="Chemical Physics Letters" /></span></a></div></div><div class="PageDivider"></div><h1 id="screen-reader-main-title" class="Head u-font-serif u-h2 u-margin-s-ver"><span class="title-text">Epstein-Nesbet second-order perturbation treatment of dynamical electron correlation and ground state potential energy curve of Cr<sub>2</sub></span></h1><div class="Banner" id="banner"><div class="wrapper truncated"><div class="AuthorGroups text-s"><div class="author-group" id="author-group"><span class="sr-only">Author links open overlay panel</span><button class="button-link button-link-primary" type="button" data-sd-ui-side-panel-opener="true" data-xocs-content-type="author" data-xocs-content-id="aep-author-id1"><span class="button-link-text"><span class="react-xocs-alternative-link"><span class="given-name">Alexander O.</span> <span class="text surname">Mitrushenkov</span> </span><span class="author-ref" id="bAFF1"><sup>a</sup></span></span></button>, <button class="button-link button-link-primary" type="button" data-sd-ui-side-panel-opener="true" data-xocs-content-type="author" data-xocs-content-id="aep-author-id2"><span class="button-link-text"><span class="react-xocs-alternative-link"><span class="given-name">Paolo</span> <span class="text surname">Palmieri</span> </span><span class="author-ref" id="bAFF2"><sup>b</sup></span></span></button></div></div></div><button class="button-link button-link-secondary u-margin-s-ver text-s show-more-button button-link-icon-right" type="button" id="show-more-btn" data-aa-button="icon-expand"><span class="button-link-text">Show more</span><svg focusable="false" viewBox="0 0 92 128" height="20" width="17.25" class="icon icon-navigate-down"><path d="m1 51l7-7 38 38 38-38 7 7-45 45z"></path></svg></button><div class="banner-options 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36h57.07l-59.5 59.5 7.07 7.08 59.36-59.36v56.78h1e1v-74h-74z"></path></svg></a></div><section class="ReferencedArticles"></section><section class="ReferencedArticles"></section><div id="preview-section-abstract"><div class="PageDivider"></div><div class="Abstracts u-font-serif text-s" id="abstracts"><div class="abstract author" id="aep-abstract-id3"><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Abstract</h2><div id="aep-abstract-sec-id4"><p id="simple-para.0010">The Cr<sub>2</sub> potential energy curve is obtained by treating the dynamical correlation energy terms using a CI procedure based on determinants, equivalent to multi-reference second-order perturbation theory with the Epstein-Nesbet partition of the Hamiltonian. One of the advantages of this treatment is that the level shifts required for the equivalent Møller-Plesset type of treatment to eliminate intruder states and avoid divergences in the ground state second-order energy expression, are not required. Moreover, by truncating the reference space, the dynamical and the non-dynamical correlation energy is included also for the 3s, 3p electrons. The potentials are compared to experiment and to the most accurate theoretical potential curves in the literature.</p></div></div></div></div><div id="preview-section-introduction"></div><div id="preview-section-snippets"></div><div class="related-content-links u-hide-from-md"><button type="button" class="button button-anchor" aria-disabled="false"><span class="button-text">Recommended articles</span></button></div><div class="Tail text-s"></div><div id="preview-section-references"><div class="paginatedReferences u-font-serif text-s"><div class="PageDivider"></div><header><h2 class="u-h4 u-margin-l-ver"><span>References</span><span> (35)</span></h2></header><ul><li class="bib-reference u-margin-s-bottom"><span class="u-font-sans"><span class="author u-font-sans"><span>V.E. </span>Bondybey</span><em> et al.</em></span><span class="host u-clr-grey6 u-font-sans"><div class="series"><h3 class="title">Chem. Phys. 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Phys.</h3></div><div class="series">(1991)</div></span></li><li class="bib-reference u-margin-s-bottom"><span class="u-font-sans"><span class="author u-font-sans"><span>H.J. </span>Werner</span><em> et al.</em></span><span class="host u-clr-grey6 u-font-sans"><div class="series"><h3 class="title">J. Chem. Phys.</h3></div><div class="series">(1988)</div></span></li></div><button class="button-alternative button-alternative-secondary text-m u-font-sans u-margin-l-bottom button-alternative-icon-left" type="button" id="show-more-refs-btn"><span class="button-alternative-icon"><svg focusable="false" viewBox="0 0 92 128" width="17.25" height="24" class="icon icon-navigate-down u-fill-grey8"><path d="m1 51l7-7 38 38 38-38 7 7-45 45z"></path></svg></span><span class="button-alternative-text">View more references</span></button></div></div><div id="preview-section-cited-by"><section aria-label="Cited by" class="ListArticles preview"><div class="PageDivider"></div><header id="citing-articles-header"><h2 class="u-h4 u-margin-l-ver u-font-serif">Cited by (21)</h2></header><div aria-describedby="citing-articles-header"><div class="citing-articles u-margin-l-bottom"><ul><li class="ListArticleItem u-margin-l-bottom"><div class="sub-heading u-margin-xs-bottom"><h3 class="u-font-serif" id="citing-articles-article-0-title"><a class="anchor anchor-default" href="/science/article/pii/S000926149901458X"><span class="anchor-text">On a mixed Møller-Plesset Epstein-Nesbet partition of the Hamiltonian to be used in multireference perturbation configuration interaction</span></a></h3><div class="text-s">2000, Chemical Physics Letters</div><div class="CitedSection u-margin-s-top"><div class="u-margin-s-left"><div class="cite-header text-s u-text-italic u-font-sans">Citation Excerpt :</div><p class="u-font-serif text-xs">The MP-EN curve (see Fig. 5) is also completely exempt from any intruder problem and shows a qualitatively correct behaviour, with the characteristic `shelf&#x27; in correspondence to the 4s–4s bonding region [26], but it is still overbound by ≈0.8 eV. Our MP-EN results are comparable with those of Mitrushenkov and Palmieri [27], who also employ an EN-type perturbation treatment. We have also experimented the imaginary level shift technique of Forsberg and Malmqvist [25]with our MPB partition (MPB+LS) and have obtained the potential curve shown in Fig. 5 at the cost of a large shift of 0.3 a.u.</p></div></div></div><div class="buttons text-s"><button class="button-link button-link-secondary button-link-icon-right" type="button" data-aa-button="sd:product:journal:article:location=citing-articles:type=view-details" aria-describedby="citing-articles-article-0-title" aria-controls="citing-articles-article-0" aria-expanded="false"><span class="button-link-text">Show abstract</span><svg focusable="false" viewBox="0 0 92 128" width="17.25" height="24" class="icon icon-navigate-down"><path d="m1 51l7-7 38 38 38-38 7 7-45 45z"></path></svg></button></div><div class="u-display-none" aria-hidden="true"><div class="abstract u-margin-xs-top u-margin-m-bottom u-font-serif text-s" id="reference-abstract"><div class="u-margin-ver-m"><p id="simple-para.0060">Within the frame of second-order multi-reference perturbation theory (MR-PT), drawing on previous work of Dyall, a new partition of the Hamiltonian, which can loosely be considered as intermediate between Møller–Plesset (MP) and Epstein–Nesbet (EN), is presented. The method, which is well suited for CAS-SCF zero-order wavefunctions, is expected to correct partially the defects of MP and EN while retaining their good properties. The new approach has been successfully applied to some test cases involving the homonuclear diatomics F<sub>2</sub>, Cl<sub>2</sub> and N<sub>2</sub> where the faults of the EN treatment appear to be in large measure eliminated. Application to the Cr<sub>2</sub> diatomic shows that the dramatic intruder state problem suffered by the MP treatment is completely solved, affording a qualitatively good description of the potential energy curve for the ground state.</p></div></div></div></li><li class="ListArticleItem u-margin-l-bottom"><div class="sub-heading u-margin-xs-bottom"><h3 class="u-font-serif" id="citing-articles-article-1-title"><a class="anchor anchor-default" href="/science/article/pii/S0301010499002104"><span class="anchor-text">Cavity ringdown spectroscopy search for transition metal dimers</span></a></h3><div class="text-s">1999, Chemical Physics</div></div><div class="buttons text-s"><button class="button-link button-link-secondary button-link-icon-right" type="button" data-aa-button="sd:product:journal:article:location=citing-articles:type=view-details" aria-describedby="citing-articles-article-1-title" aria-controls="citing-articles-article-1" aria-expanded="false"><span class="button-link-text">Show abstract</span><svg focusable="false" viewBox="0 0 92 128" width="17.25" height="24" class="icon icon-navigate-down"><path d="m1 51l7-7 38 38 38-38 7 7-45 45z"></path></svg></button></div><div class="u-display-none" aria-hidden="true"><div class="abstract u-margin-xs-top u-margin-m-bottom u-font-serif text-s" id="reference-abstract"><div class="u-margin-ver-m"><p>A reinvestigation of several isotopic species of Cr<sub>2</sub> by the cavity ringdown technique yields a frequency of Δ<em>G</em><sub>1/2</sub>=417±4 cm<sup>−1</sup> for the A <span class="math"><math><msup><mi></mi><mn>1</mn></msup><mtext>Σ</mtext><msup><mi></mi><mn>+</mn></msup><msub><mi></mi><mn><mtext>u</mtext></mn></msub></math></span> state, and casts doubt on the assignment of a band near 21 700 cm<sup>−1</sup> previously attributed to the 1–1 transition. Even though copious amounts of Ti<sub>2</sub> were produced in our source, search for its transition reported in the same spectral region in matrices yielded no positive results. For both metals investigated, extremely strong absorptions of highly excited metastable atoms were detected.</p></div></div></div></li><li class="ListArticleItem u-margin-l-bottom"><div class="sub-heading u-margin-xs-bottom"><h3 class="u-font-serif" id="citing-articles-article-2-title"><a class="anchor anchor-default" href="https://doi.org/10.1063/1.477391" target="_blank"><span class="anchor-text">Efficient truncation strategies for multi-reference configuration interaction molecular energies and properties</span><svg focusable="false" viewBox="0 0 78 128" aria-label="Opens in new window" width="1em" height="1em" class="icon icon-arrow-up-right arrow-external-link"><path d="m4 36h57.07l-59.5 59.5 7.07 7.08 59.36-59.36v56.78h1e1v-74h-74z"></path></svg></a></h3><div class="text-s">1998, Journal of Chemical Physics</div></div><div class="buttons text-s"></div><div class="u-display-none" aria-hidden="true"><div class="abstract u-margin-xs-top u-margin-m-bottom u-font-serif text-s" 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id="citing-articles-article-5-title"><a class="anchor anchor-default" href="https://doi.org/10.1063/1.4952453" target="_blank"><span class="anchor-text">The bond length and bond energy of gaseous CrW</span><svg focusable="false" viewBox="0 0 78 128" aria-label="Opens in new window" width="1em" height="1em" class="icon icon-arrow-up-right arrow-external-link"><path d="m4 36h57.07l-59.5 59.5 7.07 7.08 59.36-59.36v56.78h1e1v-74h-74z"></path></svg></a></h3><div class="text-s">2016, Journal of Chemical Physics</div></div><div class="buttons text-s"></div><div class="u-display-none" aria-hidden="true"><div class="abstract u-margin-xs-top u-margin-m-bottom u-font-serif text-s" id="reference-abstract"></div></div></li></ul><a class="button-alternative button-alternative-secondary button-alternative-icon-left" href="http://www.scopus.com/scopus/inward/citedby.url?partnerID=10&amp;rel=3.0.0&amp;eid=2-s2.0-0031592899&amp;md5=cc34ab50b2ae5deb419e25a12bf12cd" target="_blank" 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Our MP-EN results are comparable with those of Mitrushenkov and Palmieri [27], who also employ an EN-type perturbation treatment. We have also experimented the imaginary level shift technique of Forsberg and Malmqvist [25]with our MPB partition (MPB+LS) and have obtained the potential curve shown in Fig. 5 at the cost of a large shift of 0.3 a.u."],"thirdParty":false,"volume":"Volume 317","abstract":{"$$":[{"$$":[{"#name":"section-title","_":"Abstract"},{"$$":[{"$$":[{"#name":"__text__","_":"Within the frame of second-order multi-reference perturbation theory (MR-PT), drawing on previous work of Dyall, a new partition of the Hamiltonian, which can loosely be considered as intermediate between Møller–Plesset (MP) and Epstein–Nesbet (EN), is presented. The method, which is well suited for CAS-SCF zero-order wavefunctions, is expected to correct partially the defects of MP and EN while retaining their good properties. 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Even though copious amounts of Ti"},{"$":{"loc":"post"},"#name":"inf","_":"2"},{"#name":"__text__","_":" were produced in our source, search for its transition reported in the same spectral region in matrices yielded no positive results. 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Continuous strides are being made to explore materials capable of binding with helium and neon. In this report, inorganic fullerenes are studied for their ability to adsorb and encapsulate helium and neon atoms. Both endohedral and exohedral complexes of X"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":"Y"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":" with helium and neon are considered. Moreover, interconversion of exohedral and endohedral complexes is explored through an unprecedented approach where noble gases translate into the nano-cage through boundary crossing. The translation of He and Ne through the surface of X"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":"Y"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":" (X"},{"$":{"sp":"0.25"},"#name":"hsp"},{"#name":"__text__","_":"="},{"$":{"sp":"0.25"},"#name":"hsp"},{"#name":"__text__","_":"B, Al and Y"},{"$":{"sp":"0.25"},"#name":"hsp"},{"#name":"__text__","_":"="},{"$":{"sp":"0.25"},"#name":"hsp"},{"#name":"__text__","_":"N, P) nano-cages (permeability of the nano-cage) is studied theoretically at B971 method of density functional theory. The kinetic barrier for encapsulation of helium and neon is obtained through scanning potential energy surface for motion of He/Ne through hexagons of the nano-cage. The translation of He and Ne is not feasible process at room temperature however, permeation selectivity can be achieved with controlled temperature. The effect of temperature n the boundary crossing barrier is also explored. The estimate of stabilities of exohedral and endohedral complexes of He and Ne with X"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":"Y"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":" nano-cages is obtained through binding energy analysis. The exohedral binding of He/Ne with X"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":"Y"},{"$":{"loc":"post"},"#name":"inf","_":"12"},{"#name":"__text__","_":" nano-cages is a favorable process whereas the encapsulation is thermodynamically unfavorable except for Ne in AlP nano-cage. The highest interaction energy is observed for exohedral doping of Ne with AlN nano-cage (−"},{"$":{"sp":"0.10"},"#name":"hsp"},{"#name":"__text__","_":"4.86"},{"$":{"sp":"0.25"},"#name":"hsp"},{"#name":"__text__","_":"kcal"},{"$":{"sp":"0.25"},"#name":"hsp"},{"#name":"__text__","_":"mol"},{"$$":[{"#name":"__text__","_":"−"},{"$":{"sp":"0.10"},"#name":"hsp"},{"#name":"__text__","_":"1"}],"$":{"loc":"post"},"#name":"sup"},{"#name":"__text__","_":") which is comparable to Ne binding with highly electrophilic Be(CN)"},{"$":{"loc":"post"},"#name":"inf","_":"2"},{"#name":"__text__","_":". Adsorption/encapsulation energies of noble gases on/in nano-cages show strong correlation with the size of the nano-cage. The interaction energies at B97-1 method are also compared with those from M05-2X, B3LYP-D2 and PBE-D2 methods. SAPT analysis is also performed for evaluating the components of interaction energies. 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